Anomalous X-ray Diffraction Studies for Photovoltaic Applications

Grisel Rivera Batista

Department of Energy, Science Undergraduate Laboratory Internship Program

University of Puerto Rico, Río Piedras Campus

San Juan, Puerto Rico

SLAC National Accelerator Laboratory

Menlo Park, California

August 13, 2010

Prepared in partial fulfillment of the requirement of the Office of Science, Department of

Energy’s Science Undergraduate Laboratory Internship under the direction of Michael Toney,

Sumohan Misra and Joanna Bettinger in the Stanford Synchrotron Radiation Lightsource at

SLAC National Accelerator Laboratory.

Participant: ________________________________________ Signature

Research Advisor: ________________________________________ Signature

Research Advisor: ________________________________________ Signature

Research Advisor: ________________________________________ Signature

SLAC-TN-11-013

Work supported in part by US Department of Energy contract DE-AC02-76SF00515.

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TABLE OF CONTENTS

Abstract . . . . . ii

Introduction . . . . . 1

Materials and Methods . . . . 2

Results . . . . . 5

Discussion and Conclusion . . . . 5

Acknowledgements . . . . . 6

References . . . . . 6

Figures . . . . . 8

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ABSTRACT

Anomalous X-ray Diffraction Studies for Photovoltaics Applications – Solar Cells, GRISEL

RIVERA BATISTA (University of Puerto Rico, Río Piedras Campus, San Juan, PR 00931-1907)

MICHAEL TONEY, SUMOHAN MISRA, JOANNA BETTINGER (SLAC National

Accelerator Laboratory, Menlo Park, CA 94025)

Anomalous X-ray Diffraction (AXRD) has become a useful technique in characterizing bulk and

nanomaterials as it provides specific information about the crystal structure of materials. In this

project we present the results of AXRD applied to materials for photovoltaic applications: ZnO

loaded with Ga and ZnCo2O4 spinel. The X-ray diffraction data collected for various energies

were plotted in Origin software. The peaks were fitted using different functions including Pseudo

Voigt, Gaussian, and Lorentzian. This fitting provided the integrated intensity data (peaks area

values), which when plotted as a function of X-ray energies determined the material structure.

For the first analyzed sample, Ga was not incorporated into the ZnO crystal structure. For the

ZnCo2O4 spinel Co was found in one or both tetrahedral and octahedral sites.

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INTRODUCTION

The use of anomalous X-ray diffraction (AXRD) provides element and site specific information

for the crystal structure of a material. This technique lets us correlate the structure to the

electronic properties of the materials as it allows us to probe precise locations of cations in the

spinel structure. What makes it possible is that in AXRD the diffraction pattern is measured at a

number of energies near an X-ray absorption edge of an element of interest. The atomic

scattering strength of an element varies near its absorption edge and hence the total intensity of

the diffraction peak changes by changing the X-ray energy. Thus AXRD provides element

specific structural information. This method can be applied to both crystalline and liquid

materials. One of the advantages of AXRD in crystallography experiments is its sensitivity to

neighboring elements in the periodic tables. This method is also sensitive to specific

crystallographic phases and to a specific site in a phase [1].

The main use of AXRD in this study is for transparent conductors (TCs) analysis. TCs are

considered to be important materials because of their efficiency and low risk of environmental

pollution. These materials are important to solar cells as a result of their remarkable combination

of optical and electrical properties, including high electrical conductivity and high optical

transparency in the spectrum of visible light [2][3]. TCs provide a transparent window, which

allows sunlight to pass through while also allowing electricity to conduct out of the cell.

Spinel materials have the chemical form AB2O4, and are made of a face-centered cubic (FCC)

lattice of oxygen anions and cations in specific interstitial sites (see Figure 1,2) [4] [5]. A normal

spinel has all A cations on tetrahedral sites and B cations on octahedral sites. In contrast; an

inverse spinel has the A and half of the B cations on octahedral sites and the other half of the B

cations on tetrahedral sites; a mixed spinel lies between (see Figure 3). In the spinel structure, 8

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of 64 possible tetrahedral sites and 16 of 32 possible octahedral sites are filled. Normal spinels

have particularly high conduction as the linear octahedral chains of B cations likely serve as

conduction paths [2].

In this paper we present how the data obtained with AXRD is used to analyze TCs properties as

they apply to photovoltaic applications. One of the materials used for this analysis is zinc oxide.

It has been loaded with 5% and 10% of Ga, which has an absorption edge of 10367 eV. The peak

(100) was measured for the zinc oxide loaded with 10% Ga. In the case of 5% Ga, we measured

peaks (100) and (101). With the information provided by the AXRD we can identify if Ga is

being incorporated in the ZnO crystal structure. The analysis of 311 plane in the ZnCo2O4 spinel

shows if Co is in tetrahedral or octahedral site.

MATERIALS AND METHOD

Theoretical Model

In a diffraction experiment, incident X-rays are directed toward a sample of interest, and are

deflected by the atoms in the sample. The waves that are diffracted from different atoms can

interfere with each other and consist of sharp interference maxima (peaks) with the same

symmetry as in the distribution of atoms [4]. The atomic distance is an important fact in this

analysis because it is directly related to the peaks in an X-ray diffraction patterns. For a given set

of lattice planes with an inter-planar distance of d, the condition for a diffraction (peak) to occur

can be simply written as which is known as the Bragg's law.

2 sinn d (1)

3

2

, ,1

n n n

atomsi hx ky lz

nh k ln

F f E e

In this equation, λ is the wavelength of the X-ray, θ is the scattering angle, and n is an integer

representing the order of the diffraction peak (see Figure 4). It represents the scattering of

radiation from two crystal planes of a crystal. These planes behave like half-reflecting mirrors.

There is a difference of 2dsinθ in the pathlength travelled by the two beams of radiation where d

is the perpendicular distance between the planes (the path difference is marked in green and the

expanded construction alongside makes the geometry more clear). As the angle of reflection is

changed so does the difference in pathlength travelled by the two beams. When the path

difference is equal to an integer number of wavelengths the two beams will reinforce one another

and when it is an integral number of half wavelengths the two waves will interfere destructively

with one another. The intensity of the total reflected radiation will vary sinusoidally with θ

[6][7]. Understanding and application of Bragg’s Law can provide much useful information

about various samples. It can identify the lattice parameter and phase of the material. Proper

understanding of the structure factor can yield more information, particularly when combined

with X-ray absorption for AXRD measurements.

(2)

(3)

In this equation fn represents the atomic scattering factor, xn, yn, and zn are the fractional

positions of the nth

atom, f0 (Q) is the normal factor (E independent), f’(E) is the anomalous (E

dependent), and f’’(E) is the absorption (E dependent). The fn varies near X-ray absorption edge,

producing a total intensity change. One fact to be considered about fn is that it depends on

' ''

0nf f Q f E if E

4

2

hkl hklI F

oxidation state of the element [2]. Calculating the scattering factor let us know the intensity value

since both are proportional.

(4)

In this equation, the intensity, I, is equal to the square of the absolute value of the scattering

factor. For this reason, if the X-ray energy near the absorption edge is varied, then total intensity

change.

Data Analysis

The software used to develop the analysis was Origin. Once the data was collected at SSRL

beamline 2-1, we used Origin to fit peaks and obtain their integrated intensity (peaks area). As

peaks are a combination of Gaussian and Lorentzian functions, we used the Pseudo Voigt

function for fitting. Compared with Gaussian and Lorentzian functions, Pseudo Voigt gave us the

lowest standard errors in the fittingFor each data set we selected some scans to make an average

of the wG, wL, and mμ. The reason we used the average values was to keep the peak shape

constant for all X-ray energies.

When the peaks are fitted, we proceed to plot the obtained peak area values as a function of

X-ray energies. If we see a feature at an energy corresponding to the absorption edge of a

particular element, then that element is present at that particular crystallographic phase. In our

case, we are looking for Ga in ZnO, which has an absorption edge at 10367 eV, and for Co in

ZnCo2O4 spinel, which has an absorption edge at around 7709 eV. The presence of the cation in

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the graph tells us about the material structure. We can determine if the atoms are in tetrahedral or

octahedral site in the compound.

RESULTS

The average values obtained using Pseudo Voigt function were 0.5835 for wG, 1.2969 for wL, and

-0.0196 in mμ. In the case of the Gaussian and Lorentzian fitting, the average values for each w

were 0.4976 and 0.6196 respectively. For the ZnO loaded with Ga, the data obtained showed a

smooth curve in the plot of area as a function of X-ray energies. It did not show any dip at the

Ga-absorption edge (see Figures 5,6,7).

Figure 4 shows the fitting for the spinel ZnCo2O4 in 311 geometry. There is a big change around

7730 eV, which means that cobalt is present in the sample because its absorption edge is very

close to that found in the fitting (7709 eV). The 311 plane probes both tetrahedral and octahedral

sites in the spinel crystal structure, so the "dip" seen near the Co absorption edge means that Co

is found in one or both of these sites (see Figures 8,9).

DISCUSSION AND CONCLUSIONS

The absorption edge seen for ZnCo2O4 determined that Co is present in the sample in tetrahedral

and octahedral structure. It means that we can find Co2+

and Co3+

in the plane 311. With the

obtained results is clear that AXRD is a used technique for the determination of the structure of a

material since we were able to obtain the needed data to identify whether the Ga and Co were in

tetrahedral or octahedral sites. In the case of the fitting, we can conclude that diffracted peak

intensity decreases depending on elements present on diffracting planes. As the energy is varied

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through the absorption edge, there is a step function in diffracted intensity. In general, the

structural information obtained via diffraction is combined with chemical information obtained

via spectroscopy. At an absorption edge, there is a significant change in the atomic scattering

factor, which in turn affects the structure factor. Thus by scanning energy while maintaining the

Bragg condition for a particular atomic plane, it is possible to determine if certain elements are

present based on changes in scattered intensity associated with each element’s absorption edge.

ACKNOWLEDGMENTS

This work was supported by the U.S. Department of Energy, Office of Science, through the

Summer Undergraduate Laboratory Internship Program (SULI) and Stanford Synchrotron

Radiation Lightsource (SSRL) at SLAC National Accelerator Laboratory. I would especially like

to thank my mentors Michael Toney, Sumohan Misra, and Joanna Bettinger for their guidance

during the realization of my project. I would also like to thank Yezhou Shi and Rodrigo Noriega

for their help and explanations. Finally, I would also like to thank Stephen Rock and all the SULI

staff at SLAC for give me the opportunity to work during this summer under their program.

REFERENCES

[1] Bettinger, J., Misra, S. Anomalous X-ray Diffraction (AXRD), California. 2010.

[2] Bettinger, J. Probing the Effects of Dopants, Defects, and Crystal Structure in Spinel

Transparent Conducting Oxides for Photovoltaic Applicationsi, California.

[3] Granqvist, C. G., Transparent conductors as solar energy materials: A panoramic review,

Department of Engineering Sciences, The Ångström Laboratory, Uppsala University, Uppsala,

Sweeden. 2007.

[4] Pecharsky, V. K., Zavalij, P.Y., Fundamentals of Powder Diffraction and Structural

Characterization of Materials, Page 146-152, Springer, New York. 2005.

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[5] Thomas, R.K., Simple Solids and their Surfaces [Online]. Available:

http://rkt.chem.ox.ac.uk/tutorials/surfaces/solids.html

[6] Introduction to X-ray Diffraction, Materials Research laboratory, University of California,

Santa Barbara. 2010.

[7] Cullity, B.D., Stock, S.R., Elements of X-Ray Diffraction, Page 31-47, Prentice Hall, New

Jersey. 2001.

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FIGURES

(a) (b) (c)

Figure 1: (a) Model of spinel AB2O4 structure (b) Model of tetrahedral sites in the spinel (c)

Model of octahedral site in the spinel.

Figure 2: In a Face Centered Cubic (FCC) lattice the atoms are arranged at the corners and center

of each cube face of the cell.

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Figure 3: Representation of normal and inverse spinel of a ZnCo2O4. In the normal spinel Zn

atom is in tetrahedral site and both Co atoms are in octahedral sites. For the inverse spinel, Zn is

in octahedral site and atoms of Co are in tetrahedral and octahedral sites.

Figure 4: Model of Bragg’s Law. Blue lines indicates the X-ray beamed and diffracted. θ is the

angle formed by the diffraction, d is the distance between the atoms plate

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Figure 5: X-ray diffraction pattern for ZnO. The peak (100) is analyzed using Origin software.

Figure 6: Fitting of peak (100) for scan 90 of ZnO. Red line indicate the fiiting using Pseudo

Voigt function, green line indicates the fitting using Gauss function, and blue line indicate the

fitting using Lorentz function.

Q (Å-1)

2.0 2.5 3.0 3.5 4.0

Inte

nsi

ty (

a.u

.)

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18(101)

(002)

(102)

(110)

(100)

(103)

(200)

(112)

(201)

ZnO loaded with Ga

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Figure 7: Graph of integrated intensity as a function of X-ray energy. Dashed line indicate Ga

absorption edge at 10367 eV.

Figure 8: Fitting of peak (311) for scan 90 of ZnCo2O4 spinel. Red line indicate the fiiting using

Pseudo Voigt function, green line indicates the fitting using Gauss function, and blue line

indicate the fitting using Lorentz function.

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Figure 9: Graph of integrated intensity as a function of X-ray energy. Dashed line indicate Co

absorption edge at 7709 eV.